A rabbit jumps up into the air with an initial upward velocity of $12$ feet per second and lands on the ground. Therefore, the rabbit's height above the ground in feet, $t$ seconds after it jumps, can be modeled by the expression $-16t^2 + 12t$ . This expression can be written in factored form as $-16t(t - 0.75)$ . $\newline$ What does the number $0.75$ represent in the expression? $\newline$ (A)the height in feet of the rabbit when it reaches its highest point $\newline$ (B)the time in seconds from when the rabbit jumps until it reaches its highest point $\newline$ (C)the time in seconds from when the rabbit jumps until it lands on the ground $\newline$ (D)the height in feet of the rabbit at the start of its jump

Full solution

Q. A rabbit jumps up into the air with an initial upward velocity of

12

feet per second and lands on the ground. Therefore, the rabbit's height above the ground in feet,

t

seconds after it jumps, can be modeled by the expression

-16t^2 + 12t

. This expression can be written in factored form as

-16t(t - 0.75)

\newline

What does the number

0.75

represent in the expression?

\newline

(A)the height in feet of the rabbit when it reaches its highest point

\newline

(B)the time in seconds from when the rabbit jumps until it reaches its highest point

\newline

(C)the time in seconds from when the rabbit jumps until it lands on the ground

\newline

(D)the height in feet of the rabbit at the start of its jump

Expression for Rabbit's Height: The expression for the rabbit's height is $-16t^2 + 12t$ , which is equivalent to $-16t(t - 0.75)$ .
Meaning of $0.75$ : To find the meaning of $0.75$ , we look at the factored form $-16t(t - 0.75)$ . The roots of the quadratic equation represent the times when the height is zero (when the rabbit is on the ground).
Roots of Quadratic Equation: One root is $t = 0$ , which is when the rabbit just jumps. The other root is $t = 0.75$ , which is when the rabbit lands back on the ground.
Interpretation of $0.75$ : Since the roots represent the times when the rabbit's height is zero, $0.75$ represents the time in seconds from when the rabbit jumps until it lands on the ground.